-b=, 105 105x a +b=-*; .. 100 100 a translation of the enunciation, by supposing the interest additive to the capital, in which case, the sum b ought to be subtracted, This equation, treated as the preceding, shall give x=206, If the interest at 5 per cent be subtracted from 100, in which case 100 reduces itself to 95, we have the capital c at the end of the year, by the proportion 95% 100 95x consequently, +b=; 100 multiplying by 100, and transposing, we shall have 100b=5x, s. x=206. The negative isolated result, that is, the negative value of x, would announce a rectification or a correction in the terms of the enunciation, and the problem proposed could be re-established in two ways. w Prob 5. What number is that, the double of which exceeds its half by 6? = Let x=the number; 2 or 3x=12, .. by division, x=4. Prob. 6. From two towns which are 187 miles distant, two travellers set out at the same time, with an intention of meeting. One of them goes 8 miles, and the other 9 miles a day. In how many days will they meet ? Let x= the number of days required; then 8x=the number of miles one travelled, and 9x = the number the other travelled ; and since they meet, they must have travelled together the whole distance, consequently, 8x+9x=187, or 17x=187, .. by division, x=11. Prob. 7. What number is that, from which 6 being subtracted, and the remainder multiplied by 11, the product will be 121 ? Let w=the number required ; Then by the problem (-6) XH=121, by transposition, 112=121 +66, or 11x=187, .. by division, a=17. Prob. 8. A Gentleman meeting 4 poor persons, distributed five 4 shillings amongst them: to 1' second he gave twice, the third thrice, and to the fourth four times as much as to the first. What, did he give to each ? Let <= the pence he gave to the first, ..2x= the pence given to the second, and 3x = to the third, 4x to the fourth .. by the problem, uto2x+3x+4x=5X12=60, or 10x=60, by division, x=6, and therefore he gave 6, 12, 18, 24 pence respectively to them. Prob. 9. A Bookseller sold 10 books at a certain price; and afterwards 15 more at the same rate. Now at the latter time he received 35 shillings more than at the former. What did he receive for each book ? Let = the price of a book. then 10x= the price of the first set, and 15x=the price of the second set ; bat by the problem, 151=10x +35; .. by transposition, 5x=35; and by division, x=7, Prob. 10. A Gentleman dying bequeathed a legacy of 1400 dallars to three servants. A was to have twice as much as B; and B three times as much as C. What were their respective shares ? Let x=C's share, .. 3x=B's share, and 6x=A's share ; then by the problem, x+3x+6x=1400, or 10x = 1400, .. by division, x=140=C's share. ... A received 840 dollars; B, 420 dollars; and C, 140 dollars. Prob. 11. There are two numbers whose difference is 15, and their sum 59. What are the numbers ? As their difference is 15, it is evident that the greater number must exceed the lesser by 15. Let, therefore, x= the lesser number; then will +15= the greater; ... by the problem, x++15=59, or 2.+15=59, by transposition, 2x=59-15=44, ... by division, x=22 the lesser number, and x+15=22 +15=37 the greater. Prob. 12. What two numbers are those whose difference is 9; and if three times the greater be added to five times the lesser, the sum shall be 35 ? Let the lesser number; .. by the problem, (3x+27)+5x=35 or 8x=8; .. by division, x=1 the lesser number, and x+9=1+9=10 the greater number. 2 Prob. 13. What number is that, to which 10 being added, şths of ihe sum will be 66 ? 5 Let x= the number required; then x+10= the number, with 10 added to it. 3(x+10) Now ths of (~ +10)=3(x+10)=3x +30 5 3x +30 =66; 5 by multiplication, 3.x +30=330; by transposition, 3x=300; .. by division, x=100. Prob. 14. What number is that, which being multiplied by 6, the product increased by 18, and that sum divided by 9, the quotient shall be 20? x= Let x= the number required , then 6x= the number multiplied by 6; 6x +18= the product increased by 18; and 6x +18 = that sum divided by 9. 9 6x +18 .. by the problem, = 20; 9 by multiplication, 6x +18=20X9; by transposition, 6x=180-18, or 6x=162; .. by division, =27. Prob. 15. A post is {th in the earth, ths in the water, and 13 feet out of the water. What is the length of the post ? Let x= the length of the post; 2 then the part of it it in the earth, 5 3x = the part of it in the water, 7 and 13= the part of it out of the water. But by the problem, part in earth + part in water + part out of water = whole part; 3х ()+(**) +13=«. 30 and X35+ X 35+13 X 35=35x, 7 or 70 +15x+455=35x; by transposition, 455=351---7-15x=13x, or 13x = 455 ; ... by division, x=35 length of the post. Prob. 16. After paying away {th and th of my money, I had 850 dollars left. What money had I at first ? + Let in my purse at first; then money paid away. 4 7 But money at first money paid away = money remaining .. by the problem, =850, (+3) or a =850. 4 7 Multiplying by 28 the product of 4 and 7, which is the least common multiple, and 28x - *28-X 28=850 28, or 28. — 7x 4x=23800, ... 17:=23800 ; and by division, x=1400 dollars. 4 Prob. 17. What number is that, whose one half and one third plus 12, shall be equal to itself? fhen, by the problem, r= + +12; Let = the number required ; , = -+ 2 3 |